The median value of properties bought through the Help to Buy scheme over the last 15 months was £187,000. Photograph: Christopher Furlong/Getty Images

More than 4,000 households in England used the government's Help to Buy loan scheme to buy properties in June, the highest monthly total since the scheme began in 2013.

The latest government data indicated more than 4,300 completions during the month, with more than 27,100 homes bought using the scheme. The figures refer to the first phase of Help to Buy, which offers buyers an interest-free loan worth up to 20% of the price of a new-build home.

Data from the Department for Communities and Local Government showed that £1.1bn of loans had been offered, supporting purchases worth £5.65bn. More than two-thirds of buyers took the chance to take out a 95% mortgage, with the rest putting down larger deposits.

Nearly a third of sales were in the £150,001 to £200,000 price bracket, while a quarter involved homes costing less. A fifth were in the £200,001 and £250,000 bracket. The median value of properties bought through the scheme was £187,000.

Loans are available on properties costing up to £600,000 and there is no upper limit on applicants' incomes. The figures indicated that Help to Buy is not a major contributor to Britain's galloping house market. Fewer than 250 households, or 0.9% of the Help to Buy total, had used the scheme to buy properties costing more than £500,000 while 3% of the total had household incomes in excess of £100,000 a year. More than eight out of 10 purchases were made by first-time buyers.

The scheme, which went live in April 2013, was designed to kickstart construction by helping buyers with small deposits. The housing minister, Brandon Lewis, said the scheme was doing what it had been designed to achieve.

"It's no accident that since the start of the scheme private housebuilding has shot up by a third and continues to climb. Developers are increasing their output, and taking on new workers at the fastest rate since records began," he said.

Together with the second part of Help to Buy – the mortgage guarantee that applies to all homes worth up to £600,000 and not just new-builds – and the older New Buy scheme, Lewis said the government had helped almost 40,000 households to buy homes.

He added: "Today, for the first time, we're publishing postcode level data about the scheme, so communities can see exactly how this vital part of our long-term economic plan is improving the housing market and helping their area."

It found that 8,741 homes built through the scheme were in areas with a Labour MP, compared with 15,240 in Conservative constituencies. While the Conservatives had 54% more constituencies, there were 74% more Help to Buy new-builds funded in those areas.

Local authority level data showed 469 homebuyers in Wiltshire have used equity loans to buy new home, and 427 in central Bedfordshire. However, in London where the housing crisis is most acute, six boroughs have recorded no sales through the Help to Buy equity loan, including the capital's most expensive neighbourhoods of Westminster and Kensington and Chelsea. In Hammersmith and Fulham, one household had completed through the scheme by the end of June, using a loan of more than £100,000 to support their purchase.

Stewart Baseley, executive chairman of the Home Builders Federation, said Help to Buy was helping builders to supply more homes. "Indicators suggest increases in house building activity in the region of 25% and the past year has seen the steepest increase in new housing starts for around 40 years," he said. "The industry has recruited thousands of people in recent months and is working with its supply chain to ensure the capacity is there to sustain increases – all of which is giving the country a huge economic boost."

However, Baseley said for this to be sustainable central and local government needed to make sure that the planning system supported future demand for homes.

Grainne Gilmore, head of UK residential research at Knight Frank, said: "Regardless of where the take-up of Help to Buy is across the country, there are strong signs that the Equity Loan scheme is leading to a much-needed pick-up in planning permissions, which should lead to a rise in the number of homes being built in the coming years."